Subgroups — C₅₃×#36735 #27244247

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2747	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2739	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2737	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2737	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2717	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2703	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2697	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2696	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2693	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2688	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2686	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2684	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2678	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2672	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2670	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2665	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2661	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2597	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2578	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2557	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2557	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2477	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2476	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2474	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2471	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2333	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#397	C₂²	1	1	yes	characteristic
60	C₅₃×#397	C₂²	1	1	yes	characteristic
61	C₅₃×#397	C₂²	1	1	yes	characteristic
62	C₅₃×#397	C₂²	1	1	yes	characteristic
63	C₅₃×#397	C₂²	1	1	yes	characteristic
64	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#396	C₂²	1	1	yes	characteristic
72	C₅₃×#396	C₂²	1	1	yes	characteristic
73	C₅₃×#396	C₂²	1	1	yes	characteristic
74	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#394	C₂²	1	1	yes	characteristic
79	C₅₃×#394	C₂²	1	1	yes	characteristic
80	C₅₃×#394	C₂²	1	1	yes	characteristic
81	C₅₃×#394	C₂²	1	1	yes	characteristic
82	C₅₃×#394	C₂²	1	1	yes	characteristic
83	C₅₃×#394	C₂²	1	1	yes	characteristic
84	C₅₃×#394	C₂²	1	1	yes	characteristic
85	C₅₃×#394	C₂²	1	1	yes	characteristic
86	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#393	C₂²	1	1	yes	characteristic
89	C₅₃×#393	C₂²	1	1	yes	characteristic
90	C₅₃×#393	C₂²	1	1	yes	characteristic
91	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#392	C₂²	1	1	yes	characteristic
94	C₅₃×#392	C₂²	1	1	yes	characteristic
95	C₅₃×#392	C₂²	1	1	yes	characteristic
96	C₅₃×#392	C₂²	1	1	yes	characteristic
97	C₅₃×#392	C₂²	1	1	yes	characteristic
98	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#390	C₂²	1	1	yes	characteristic
102	C₅₃×#390	C₂²	1	1	yes	characteristic
103	C₅₃×#390	C₂²	1	1	yes	characteristic
104	C₅₃×#390	C₂²	1	1	yes	characteristic
105	C₅₃×#390	C₂²	1	1	yes	characteristic
106	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#388	C₂²	1	1	yes	characteristic
110	C₅₃×#388	C₂²	1	1	yes	characteristic
111	C₅₃×#388	C₂²	1	1	yes	characteristic
112	C₅₃×#388	C₂²	1	1	yes	characteristic
113	C₅₃×#388	C₂²	1	1	yes	characteristic
114	C₅₃×#388	C₂²	1	1	yes	characteristic
115	C₅₃×#388	C₂²	1	1	yes	characteristic
116	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	C₂²	1	1	yes	characteristic
145	C₅₃×#386	C₂²	1	1	yes	characteristic
146	C₅₃×#386	C₂²	1	1	yes	characteristic
147	C₅₃×#386	C₂²	1	1	yes	characteristic
148	C₅₃×#386	C₂²	1	1	yes	characteristic
149	C₅₃×#386	C₂²	1	1	yes	characteristic
150	C₅₃×#386	C₂²	1	1	yes	characteristic
151	C₅₃×#386	C₂²	1	1	yes	characteristic
152	C₅₃×#386	C₂²	1	1	yes	characteristic
153	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#381	C₂²	1	1	yes	characteristic
165	C₅₃×#381	C₂²	1	1	yes	characteristic
166	C₅₃×#381	C₂²	1	1	yes	characteristic
167	C₅₃×#381	C₂²	1	1	yes	characteristic
168	C₅₃×#380	C₂²	1	1	yes	characteristic
169	C₅₃×#380	C₂²	1	1	yes	characteristic
170	C₅₃×#380	C₂²	1	1	yes	characteristic
171	C₅₃×#380	C₂²	1	1	yes	characteristic
172	C₅₃×#380	C₂²	1	1	yes	characteristic
173	C₅₃×#380	C₂²	1	1	yes	characteristic
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#379	C₂²	1	1	yes	characteristic
177	C₅₃×#379	C₂²	1	1	yes	characteristic
178	C₅₃×#379	C₂²	1	1	yes	characteristic
179	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	—	2	4	no	—
203	C₂³×C₄×C₅₃	—	4	2	no	—
204	C₂³×C₄×C₅₃	—	4	2	no	—
205	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	#124×C₅₃	—	4	2	no	—
215	#124×C₅₃	—	4	2	no	—
216	#124×C₅₃	—	4	2	no	—
217	#123×C₅₃	—	2	4	no	—
218	#123×C₅₃	—	4	2	no	—
219	#123×C₅₃	—	4	2	no	—
220	#123×C₅₃	—	4	2	no	—
221	#123×C₅₃	—	4	2	no	—
222	C₂²⋊Q₈×C₅₃	—	4	2	no	—
223	#121×C₅₃	—	2	4	no	—
224	#121×C₅₃	—	4	2	no	—
225	#121×C₅₃	—	4	2	no	—
226	#121×C₅₃	—	4	2	no	—
227	#120×C₅₃	—	4	2	no	—
228	#120×C₅₃	—	4	2	no	—
229	#120×C₅₃	—	4	2	no	—
230	#117×C₅₃	—	4	2	no	—
231	#117×C₅₃	—	4	2	no	—
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	C₂⁴×C₅₃	—	2	2	no	—
364	C₂⁴×C₅₃	—	2	2	no	—
365	C₂⁴×C₅₃	—	2	2	no	—
366	C₂⁴×C₅₃	—	4	1	no	—
367	C₂⁴×C₅₃	—	4	1	no	—
368	C₂⁴×C₅₃	—	4	1	no	—
369	C₂⁴×C₅₃	—	4	1	no	—
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×Q₈×C₅₃	—	4	1	no	—
377	C₂×Q₈×C₅₃	—	4	1	no	—
378	C₂×Q₈×C₅₃	—	4	1	no	—
379	C₂×Q₈×C₅₃	—	4	1	no	—
380	C₂×Q₈×C₅₃	—	4	1	no	—
381	C₂×Q₈×C₅₃	—	4	1	no	—
382	C₂×D₄×C₅₃	—	2	2	no	—
383	C₂×D₄×C₅₃	—	2	2	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	2	2	no	—
387	C₂×D₄×C₅₃	—	2	2	no	—
388	C₂×D₄×C₅₃	—	2	2	no	—
389	C₂×D₄×C₅₃	—	2	2	no	—
390	C₂×D₄×C₅₃	—	2	2	no	—
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	4	1	no	—
393	C₂×D₄×C₅₃	—	4	1	no	—
394	C₂×D₄×C₅₃	—	4	1	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂×D₄×C₅₃	—	4	1	no	—
399	C₂×D₄×C₅₃	—	4	1	no	—
400	C₂×D₄×C₅₃	—	4	1	no	—
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂×D₄×C₅₃	—	4	1	no	—
406	C₂×D₄×C₅₃	—	4	1	no	—
407	C₂×D₄×C₅₃	—	4	1	no	—
408	C₂×D₄×C₅₃	—	4	1	no	—
409	C₂×D₄×C₅₃	—	4	1	no	—
410	C₂×D₄×C₅₃	—	4	1	no	—
411	C₂×D₄×C₅₃	—	4	1	no	—
412	C₂×D₄×C₅₃	—	4	1	no	—
413	C₂×D₄×C₅₃	—	4	1	no	—
414	C₂×D₄×C₅₃	—	4	1	no	—
415	C₂×D₄×C₅₃	—	4	1	no	—
416	C₂×D₄×C₅₃	—	4	1	no	—
417	C₂×D₄×C₅₃	—	4	1	no	—
418	C₂²×C₄×C₅₃	—	2	2	no	—
419	C₂²×C₄×C₅₃	—	2	2	no	—
420	C₂²×C₄×C₅₃	—	2	2	no	—
421	C₂²×C₄×C₅₃	—	2	2	no	—
422	C₂²×C₄×C₅₃	—	2	2	no	—
423	C₂²×C₄×C₅₃	—	2	2	no	—
424	C₂²×C₄×C₅₃	—	2	2	no	—
425	C₂²×C₄×C₅₃	—	2	2	no	—
426	C₂²×C₄×C₅₃	—	2	2	no	—
427	C₂²×C₄×C₅₃	—	2	2	no	—
428	C₂²×C₄×C₅₃	—	4	1	no	—
429	C₂²×C₄×C₅₃	—	4	1	no	—
430	C₂²×C₄×C₅₃	—	4	1	no	—
431	C₂²×C₄×C₅₃	—	4	1	no	—
432	C₂²×C₄×C₅₃	—	4	1	no	—
433	C₂²×C₄×C₅₃	—	4	1	no	—
434	C₂²×C₄×C₅₃	—	4	1	no	—
435	C₂²×C₄×C₅₃	—	4	1	no	—
436	C₂²×C₄×C₅₃	—	4	1	no	—
437	C₂²×C₄×C₅₃	—	4	1	no	—
438	C₂²×C₄×C₅₃	—	4	1	no	—
439	C₂²×C₄×C₅₃	—	4	1	no	—
440	C₂²×C₄×C₅₃	—	4	1	no	—
441	C₂²×C₄×C₅₃	—	4	1	no	—
442	C₂²×C₄×C₅₃	—	4	1	no	—
443	C₂²×C₄×C₅₃	—	4	1	no	—
444	C₂²×C₄×C₅₃	—	4	16	no	—
445	C₂²×C₄×C₅₃	#41	1	4	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₄⋊C₄×C₅₃	—	2	2	no	—
472	C₄⋊C₄×C₅₃	—	2	2	no	—
473	C₄⋊C₄×C₅₃	—	2	2	no	—
474	C₄⋊C₄×C₅₃	—	2	2	no	—
475	C₄⋊C₄×C₅₃	—	2	2	no	—
476	C₄⋊C₄×C₅₃	—	2	2	no	—
477	C₄⋊C₄×C₅₃	—	4	1	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₄⋊C₄×C₅₃	—	4	1	no	—
483	C₄⋊C₄×C₅₃	—	4	1	no	—
484	C₄⋊C₄×C₅₃	—	4	1	no	—
485	C₄⋊C₄×C₅₃	—	4	1	no	—
486	C₄⋊C₄×C₅₃	—	4	1	no	—
487	C₄⋊C₄×C₅₃	—	4	1	no	—
488	C₄⋊C₄×C₅₃	—	4	1	no	—
489	C₄⋊C₄×C₅₃	—	4	1	no	—
490	C₄⋊C₄×C₅₃	—	4	1	no	—
491	C₄⋊C₄×C₅₃	—	4	1	no	—
492	C₄⋊C₄×C₅₃	—	4	1	no	—
493	C₄⋊C₄×C₅₃	—	4	1	no	—
494	C₄⋊C₄×C₅₃	—	4	1	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₂²⋊C₄×C₅₃	—	2	2	no	—
499	C₂²⋊C₄×C₅₃	—	2	2	no	—
500	C₂²⋊C₄×C₅₃	—	2	2	no	—
501	C₂²⋊C₄×C₅₃	—	2	2	no	—
502	C₂²⋊C₄×C₅₃	—	2	2	no	—
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	2	2	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	2	no	—
508	C₂²⋊C₄×C₅₃	—	2	2	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	4	1	no	—
512	C₂²⋊C₄×C₅₃	—	4	1	no	—
513	C₂²⋊C₄×C₅₃	—	4	1	no	—
514	C₂²⋊C₄×C₅₃	—	4	1	no	—
515	C₂²⋊C₄×C₅₃	—	4	1	no	—
516	C₂²⋊C₄×C₅₃	—	4	1	no	—
517	C₂²⋊C₄×C₅₃	—	4	1	no	—
518	C₂²⋊C₄×C₅₃	—	4	1	no	—
519	C₂²⋊C₄×C₅₃	—	4	1	no	—
520	C₂²⋊C₄×C₅₃	—	4	1	no	—
521	C₂²⋊C₄×C₅₃	—	4	1	no	—
522	C₂²⋊C₄×C₅₃	—	4	1	no	—
523	C₂²⋊C₄×C₅₃	—	4	1	no	—
524	C₂²⋊C₄×C₅₃	—	4	1	no	—
525	C₂²⋊C₄×C₅₃	—	4	1	no	—
526	C₂²⋊C₄×C₅₃	—	4	1	no	—
527	C₂²⋊C₄×C₅₃	—	4	1	no	—
528	C₂²⋊C₄×C₅₃	—	4	1	no	—
529	C₂²⋊C₄×C₅₃	—	4	1	no	—
530	C₂²⋊C₄×C₅₃	—	4	1	no	—
531	C₂²⋊C₄×C₅₃	—	4	1	no	—
532	C₂²⋊C₄×C₅₃	—	4	1	no	—
533	C₂²⋊C₄×C₅₃	—	4	1	no	—
534	C₂²⋊C₄×C₅₃	—	4	1	no	—
535	C₂²⋊C₄×C₅₃	—	4	1	no	—
536	C₂²⋊C₄×C₅₃	—	4	1	no	—
537	C₂²⋊C₄×C₅₃	—	4	1	no	—
538	C₂²⋊C₄×C₅₃	—	4	1	no	—
539	C₂²⋊C₄×C₅₃	—	4	1	no	—
540	C₂²⋊C₄×C₅₃	—	4	1	no	—
541	C₂²⋊C₄×C₅₃	—	4	1	no	—
542	C₂²⋊C₄×C₅₃	—	4	1	no	—
543	C₂²⋊C₄×C₅₃	—	4	1	no	—
544	C₂²⋊C₄×C₅₃	—	4	1	no	—
545	C₂²⋊C₄×C₅₃	—	4	1	no	—
546	C₂²⋊C₄×C₅₃	—	4	1	no	—
547	C₂²⋊C₄×C₅₃	—	4	1	no	—
548	C₂²⋊C₄×C₅₃	—	4	1	no	—
549	C₄²×C₅₃	—	4	1	no	—
550	C₄²×C₅₃	—	4	1	no	—
551	C₄²×C₅₃	—	4	1	no	—
552	C₄²×C₅₃	—	4	1	no	—
553	C₄²×C₅₃	—	4	1	no	—
554	C₄²×C₅₃	—	4	1	no	—
555	C₄²×C₅₃	—	4	1	no	—
556	C₄²×C₅₃	—	4	1	no	—
557	C₄²×C₅₃	—	4	1	no	—
558	C₂³×C₅₃	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	—	2	1	no	—
564	C₂³×C₅₃	—	2	1	no	—
565	C₂³×C₅₃	—	2	1	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	—	2	1	no	—
574	C₂³×C₅₃	—	2	1	no	—
575	C₂³×C₅₃	—	2	1	no	—
576	C₂³×C₅₃	—	2	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	1	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	4	4	no	—
598	C₂³×C₅₃	—	4	4	no	—
599	C₂³×C₅₃	—	4	4	no	—
600	C₂³×C₅₃	—	4	4	no	—
601	C₂³×C₅₃	—	4	4	no	—
602	C₂³×C₅₃	—	4	4	no	—
603	C₂³×C₅₃	—	4	4	no	—
604	C₂³×C₅₃	C₂×#41	1	2	yes	—
605	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
606	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
607	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
608	Q₈×C₅₃	—	8	2	no	—
609	Q₈×C₅₃	—	8	2	no	—
610	D₄×C₅₃	—	8	2	no	—
611	D₄×C₅₃	—	8	2	no	—
612	D₄×C₅₃	—	8	2	no	—
613	D₄×C₅₃	—	8	2	no	—
614	D₄×C₅₃	—	8	2	no	—
615	D₄×C₅₃	—	8	2	no	—
616	D₄×C₅₃	—	8	2	no	—
617	D₄×C₅₃	—	8	2	no	—
618	D₄×C₅₃	—	8	2	no	—
619	D₄×C₅₃	—	8	2	no	—
620	D₄×C₅₃	—	8	2	no	—
621	D₄×C₅₃	—	8	2	no	—
622	C₂×C₄×C₅₃	—	2	8	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	2	1	no	—
685	C₂×C₄×C₅₃	—	2	1	no	—
686	C₂×C₄×C₅₃	—	2	1	no	—
687	C₂×C₄×C₅₃	—	2	1	no	—
688	C₂×C₄×C₅₃	—	2	1	no	—
689	C₂×C₄×C₅₃	—	2	1	no	—
690	C₂×C₄×C₅₃	—	2	1	no	—
691	C₂×C₄×C₅₃	—	2	1	no	—
692	C₂×C₄×C₅₃	—	2	1	no	—
693	C₂×C₄×C₅₃	—	2	1	no	—
694	C₂×C₄×C₅₃	—	2	1	no	—
695	C₂×C₄×C₅₃	—	4	4	no	—
696	C₂×C₄×C₅₃	—	4	4	no	—
697	C₂×C₄×C₅₃	—	4	4	no	—
698	C₂×C₄×C₅₃	—	4	4	no	—
699	C₂×C₄×C₅₃	—	4	4	no	—
700	C₂×C₄×C₅₃	—	8	2	no	—
701	C₂×C₄×C₅₃	—	8	2	no	—
702	C₂×C₄×C₅₃	—	8	2	no	—
703	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
704	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
705	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
706	#36735	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
707	C₂²×C₅₃	—	2	2	no	—
708	C₂²×C₅₃	—	2	2	no	—
709	C₂²×C₅₃	—	2	2	no	—
710	C₂²×C₅₃	—	2	2	no	—
711	C₂²×C₅₃	—	2	2	no	—
712	C₂²×C₅₃	—	2	2	no	—
713	C₂²×C₅₃	—	2	2	no	—
714	C₂²×C₅₃	—	2	2	no	—
715	C₂²×C₅₃	—	2	2	no	—
716	C₂²×C₅₃	—	4	16	no	—
717	C₂²×C₅₃	—	4	1	no	—
718	C₂²×C₅₃	—	4	1	no	—
719	C₂²×C₅₃	—	4	1	no	—
720	C₂²×C₅₃	—	4	1	no	—
721	C₂²×C₅₃	—	4	1	no	—
722	C₂²×C₅₃	—	4	1	no	—
723	C₂²×C₅₃	—	4	1	no	—
724	C₂²×C₅₃	—	4	1	no	—
725	C₂²×C₅₃	—	4	1	no	—
726	C₂²×C₅₃	—	4	1	no	—
727	C₂²×C₅₃	—	4	1	no	—
728	C₂²×C₅₃	—	4	1	no	—
729	C₂²×C₅₃	—	4	1	no	—
730	C₂²×C₅₃	—	4	1	no	—
731	C₂²×C₅₃	—	4	1	no	—
732	C₂²×C₅₃	—	4	1	no	—
733	C₂²×C₅₃	—	4	1	no	—
734	C₂²×C₅₃	—	4	1	no	—
735	C₂²×C₅₃	—	4	1	no	—
736	C₂²×C₅₃	—	4	1	no	—
737	C₂²×C₅₃	—	4	1	no	—
738	C₂²×C₅₃	—	4	1	no	—
739	C₂²×C₅₃	—	4	1	no	—
740	C₂²×C₅₃	—	4	1	no	—
741	C₂²×C₅₃	—	4	1	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
751	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
752	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂²×C₅₃	#585	1	1	yes	characteristic
755	C₂²×C₅₃	#585	1	1	yes	characteristic
756	C₂²×C₅₃	#585	1	1	yes	characteristic
757	C₄×C₅₃	—	2	2	no	—
758	C₄×C₅₃	—	2	2	no	—
759	C₄×C₅₃	—	2	2	no	—
760	C₄×C₅₃	—	4	1	no	—
761	C₄×C₅₃	—	4	1	no	—
762	C₄×C₅₃	—	4	1	no	—
763	C₄×C₅₃	—	4	1	no	—
764	C₄×C₅₃	—	4	1	no	—
765	C₄×C₅₃	—	4	1	no	—
766	C₄×C₅₃	—	4	1	no	—
767	C₄×C₅₃	—	4	1	no	—
768	C₄×C₅₃	—	4	1	no	—
769	C₄×C₅₃	—	4	1	no	—
770	C₄×C₅₃	—	4	1	no	—
771	C₄×C₅₃	—	4	1	no	—
772	C₄×C₅₃	—	4	1	no	—
773	C₄×C₅₃	—	4	1	no	—
774	C₄×C₅₃	—	4	1	no	—
775	C₄×C₅₃	—	4	1	no	—
776	C₄×C₅₃	—	4	1	no	—
777	C₄×C₅₃	—	4	1	no	—
778	C₄×C₅₃	—	4	1	no	—
779	C₄×C₅₃	—	4	1	no	—
780	C₄×C₅₃	—	4	1	no	—
781	C₄×C₅₃	—	4	1	no	—
782	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
783	#2847	C₂×C₅₃	1	1	yes	characteristic, complemented
784	#2747	C₂×C₅₃	1	1	yes	characteristic, complemented
785	#2740	C₂×C₅₃	1	1	yes	characteristic, complemented
786	#2739	C₂×C₅₃	1	1	yes	characteristic, complemented
787	#2737	C₂×C₅₃	1	1	yes	characteristic, complemented
788	#2737	C₂×C₅₃	1	1	yes	characteristic, complemented
789	#2717	C₂×C₅₃	1	1	yes	characteristic, complemented
790	#2703	C₂×C₅₃	1	1	yes	characteristic, complemented
791	#2697	C₂×C₅₃	1	1	yes	characteristic, complemented
792	#2696	C₂×C₅₃	1	1	yes	characteristic, complemented
793	#2693	C₂×C₅₃	1	1	yes	characteristic, complemented
794	#2688	C₂×C₅₃	1	1	yes	characteristic, complemented
795	#2686	C₂×C₅₃	1	1	yes	characteristic, complemented
796	#2684	C₂×C₅₃	1	1	yes	characteristic, complemented
797	#2678	C₂×C₅₃	1	1	yes	characteristic, complemented
798	#2672	C₂×C₅₃	1	1	yes	characteristic, complemented
799	#2670	C₂×C₅₃	1	1	yes	characteristic, complemented
800	#2665	C₂×C₅₃	1	1	yes	characteristic, complemented
801	#2661	C₂×C₅₃	1	1	yes	characteristic, complemented
802	#2597	C₂×C₅₃	1	1	yes	characteristic, complemented
803	#2578	C₂×C₅₃	1	1	yes	characteristic, complemented
804	#2557	C₂×C₅₃	1	1	yes	characteristic, complemented
805	#2557	C₂×C₅₃	1	1	yes	characteristic, complemented
806	#2477	C₂×C₅₃	1	1	yes	characteristic, complemented
807	#2476	C₂×C₅₃	1	1	yes	characteristic, complemented
808	#2474	C₂×C₅₃	1	1	yes	characteristic, complemented
809	#2471	C₂×C₅₃	1	1	yes	characteristic, complemented
810	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
811	#2333	C₂×C₅₃	1	1	yes	characteristic, complemented
812	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
813	C₂×C₅₃	—	4	2	no	—
814	C₂×C₅₃	—	4	2	no	—
815	C₂×C₅₃	—	4	2	no	—
816	C₂×C₅₃	—	8	1	no	—
817	C₂×C₅₃	—	8	1	no	—
818	C₂×C₅₃	—	8	1	no	—
819	C₂×C₅₃	#3455	1	1	yes	characteristic
820	C₂×C₅₃	#3490	1	1	yes	characteristic
821	C₂×C₅₃	#3494	1	1	yes	characteristic
822	C₂×C₅₃	#3533	1	1	yes	characteristic
823	C₂×C₅₃	#3534	1	1	yes	characteristic
824	C₂×C₅₃	#3540	1	1	yes	characteristic
825	C₂×C₅₃	#3542	1	1	yes	characteristic
826	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
827	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
828	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
829	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
830	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
831	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
832	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
833	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
834	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
835	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
836	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
837	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
838	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
839	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
840	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
841	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
842	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
843	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
844	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
845	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
849	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
851	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
853	#397	C₂²×C₅₃	1	1	yes	characteristic
854	#397	C₂²×C₅₃	1	1	yes	characteristic
855	#397	C₂²×C₅₃	1	1	yes	characteristic
856	#397	C₂²×C₅₃	1	1	yes	characteristic
857	#397	C₂²×C₅₃	1	1	yes	characteristic
858	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
864	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
865	#396	C₂²×C₅₃	1	1	yes	characteristic
866	#396	C₂²×C₅₃	1	1	yes	characteristic
867	#396	C₂²×C₅₃	1	1	yes	characteristic
868	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
872	#394	C₂²×C₅₃	1	1	yes	characteristic
873	#394	C₂²×C₅₃	1	1	yes	characteristic
874	#394	C₂²×C₅₃	1	1	yes	characteristic
875	#394	C₂²×C₅₃	1	1	yes	characteristic
876	#394	C₂²×C₅₃	1	1	yes	characteristic
877	#394	C₂²×C₅₃	1	1	yes	characteristic
878	#394	C₂²×C₅₃	1	1	yes	characteristic
879	#394	C₂²×C₅₃	1	1	yes	characteristic
880	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#393	C₂²×C₅₃	1	1	yes	characteristic
883	#393	C₂²×C₅₃	1	1	yes	characteristic
884	#393	C₂²×C₅₃	1	1	yes	characteristic
885	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
886	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#392	C₂²×C₅₃	1	1	yes	characteristic
888	#392	C₂²×C₅₃	1	1	yes	characteristic
889	#392	C₂²×C₅₃	1	1	yes	characteristic
890	#392	C₂²×C₅₃	1	1	yes	characteristic
891	#392	C₂²×C₅₃	1	1	yes	characteristic
892	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
893	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#390	C₂²×C₅₃	1	1	yes	characteristic
896	#390	C₂²×C₅₃	1	1	yes	characteristic
897	#390	C₂²×C₅₃	1	1	yes	characteristic
898	#390	C₂²×C₅₃	1	1	yes	characteristic
899	#390	C₂²×C₅₃	1	1	yes	characteristic
900	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#388	C₂²×C₅₃	1	1	yes	characteristic
904	#388	C₂²×C₅₃	1	1	yes	characteristic
905	#388	C₂²×C₅₃	1	1	yes	characteristic
906	#388	C₂²×C₅₃	1	1	yes	characteristic
907	#388	C₂²×C₅₃	1	1	yes	characteristic
908	#388	C₂²×C₅₃	1	1	yes	characteristic
909	#388	C₂²×C₅₃	1	1	yes	characteristic
910	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
915	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#386	C₂²×C₅₃	1	1	yes	characteristic
932	#386	C₂²×C₅₃	1	1	yes	characteristic
933	#386	C₂²×C₅₃	1	1	yes	characteristic
934	#386	C₂²×C₅₃	1	1	yes	characteristic
935	#386	C₂²×C₅₃	1	1	yes	characteristic
936	#386	C₂²×C₅₃	1	1	yes	characteristic
937	#386	C₂²×C₅₃	1	1	yes	characteristic
938	#386	C₂²×C₅₃	1	1	yes	characteristic
939	#386	C₂²×C₅₃	1	1	yes	characteristic
940	#386	C₂²×C₅₃	1	1	yes	characteristic
941	#386	C₂²×C₅₃	1	1	yes	characteristic
942	#386	C₂²×C₅₃	1	1	yes	characteristic
943	#386	C₂²×C₅₃	1	1	yes	characteristic
944	#386	C₂²×C₅₃	1	1	yes	characteristic
945	#386	C₂²×C₅₃	1	1	yes	characteristic
946	#386	C₂²×C₅₃	1	1	yes	characteristic
947	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#385	C₂²×C₅₃	1	1	yes	characteristic
952	#385	C₂²×C₅₃	1	1	yes	characteristic
953	#385	C₂²×C₅₃	1	1	yes	characteristic
954	#385	C₂²×C₅₃	1	1	yes	characteristic
955	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#381	C₂²×C₅₃	1	1	yes	characteristic
959	#381	C₂²×C₅₃	1	1	yes	characteristic
960	#381	C₂²×C₅₃	1	1	yes	characteristic
961	#381	C₂²×C₅₃	1	1	yes	characteristic
962	#380	C₂²×C₅₃	1	1	yes	characteristic
963	#380	C₂²×C₅₃	1	1	yes	characteristic
964	#380	C₂²×C₅₃	1	1	yes	characteristic
965	#380	C₂²×C₅₃	1	1	yes	characteristic
966	#380	C₂²×C₅₃	1	1	yes	characteristic
967	#380	C₂²×C₅₃	1	1	yes	characteristic
968	#380	C₂²×C₅₃	1	1	yes	characteristic
969	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#379	C₂²×C₅₃	1	1	yes	characteristic
971	#379	C₂²×C₅₃	1	1	yes	characteristic
972	#379	C₂²×C₅₃	1	1	yes	characteristic
973	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
975	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
976	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
977	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
978	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	C₅₃	#36735	1	1	yes	characteristic, direct product factor, Sylow
982	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
983	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
984	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
985	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
986	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
991	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
992	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
993	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂³×C₄	—	2	4	no	—
998	C₂³×C₄	—	4	2	no	—
999	C₂³×C₄	—	4	2	no	—
1000	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	#124	—	4	2	no	—
1010	#124	—	4	2	no	—
1011	#124	—	4	2	no	—
1012	#123	—	2	4	no	—
1013	#123	—	4	2	no	—
1014	#123	—	4	2	no	—
1015	#123	—	4	2	no	—
1016	#123	—	4	2	no	—
1017	C₂²⋊Q₈	—	4	2	no	—
1018	#121	—	2	4	no	—
1019	#121	—	4	2	no	—
1020	#121	—	4	2	no	—
1021	#121	—	4	2	no	—
1022	#120	—	4	2	no	—
1023	#120	—	4	2	no	—
1024	#120	—	4	2	no	—
1025	#117	—	4	2	no	—
1026	#117	—	4	2	no	—
1027	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1114	#95	C₂³×C₅₃	1	1	yes	characteristic
1115	#95	C₂³×C₅₃	1	1	yes	characteristic
1116	#95	C₂³×C₅₃	1	1	yes	characteristic
1117	#95	C₂³×C₅₃	1	1	yes	characteristic
1118	#95	C₂³×C₅₃	1	1	yes	characteristic
1119	#95	C₂³×C₅₃	1	1	yes	characteristic
1120	#95	C₂³×C₅₃	1	1	yes	characteristic
1121	#95	C₂³×C₅₃	1	1	yes	characteristic
1122	#95	C₂³×C₅₃	1	1	yes	characteristic
1123	#95	C₂³×C₅₃	1	1	yes	characteristic
1124	#95	C₂³×C₅₃	1	1	yes	characteristic
1125	#95	C₂³×C₅₃	1	1	yes	characteristic
1126	#95	C₂³×C₅₃	1	1	yes	characteristic
1127	#95	C₂³×C₅₃	1	1	yes	characteristic
1128	#95	C₂³×C₅₃	1	1	yes	characteristic
1129	#95	C₂³×C₅₃	1	1	yes	characteristic
1130	#95	C₂³×C₅₃	1	1	yes	characteristic
1131	#95	C₂³×C₅₃	1	1	yes	characteristic
1132	#95	C₂³×C₅₃	1	1	yes	characteristic
1133	#95	C₂³×C₅₃	1	1	yes	characteristic
1134	#95	C₂³×C₅₃	1	1	yes	characteristic
1135	#95	C₂³×C₅₃	1	1	yes	characteristic
1136	#95	C₂³×C₅₃	1	1	yes	characteristic
1137	#95	C₂³×C₅₃	1	1	yes	characteristic
1138	#95	C₂³×C₅₃	1	1	yes	characteristic
1139	#95	C₂³×C₅₃	1	1	yes	characteristic
1140	#95	C₂³×C₅₃	1	1	yes	characteristic
1141	#95	C₂³×C₅₃	1	1	yes	characteristic
1142	#95	C₂³×C₅₃	1	1	yes	characteristic
1143	#95	C₂³×C₅₃	1	1	yes	characteristic
1144	#95	C₂³×C₅₃	1	1	yes	characteristic
1145	#95	C₂³×C₅₃	1	1	yes	characteristic
1146	#95	C₂³×C₅₃	1	1	yes	characteristic
1147	#95	C₂³×C₅₃	1	1	yes	characteristic
1148	#95	C₂³×C₅₃	1	1	yes	characteristic
1149	#95	C₂³×C₅₃	1	1	yes	characteristic
1150	#95	C₂³×C₅₃	1	1	yes	characteristic
1151	#95	C₂³×C₅₃	1	1	yes	characteristic
1152	#95	C₂³×C₅₃	1	1	yes	characteristic
1153	#95	C₂³×C₅₃	1	1	yes	characteristic
1154	#95	C₂³×C₅₃	1	1	yes	characteristic
1155	#95	C₂³×C₅₃	1	1	yes	characteristic
1156	#95	C₂³×C₅₃	1	1	yes	characteristic
1157	#95	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂⁴	—	2	2	no	—
1159	C₂⁴	—	2	2	no	—
1160	C₂⁴	—	2	2	no	—
1161	C₂⁴	—	4	1	no	—
1162	C₂⁴	—	4	1	no	—
1163	C₂⁴	—	4	1	no	—
1164	C₂⁴	—	4	1	no	—
1165	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1166	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1167	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1168	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1169	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1170	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1171	C₂×Q₈	—	4	1	no	—
1172	C₂×Q₈	—	4	1	no	—
1173	C₂×Q₈	—	4	1	no	—
1174	C₂×Q₈	—	4	1	no	—
1175	C₂×Q₈	—	4	1	no	—
1176	C₂×Q₈	—	4	1	no	—
1177	C₂×D₄	—	2	2	no	—
1178	C₂×D₄	—	2	2	no	—
1179	C₂×D₄	—	2	2	no	—
1180	C₂×D₄	—	2	2	no	—
1181	C₂×D₄	—	2	2	no	—
1182	C₂×D₄	—	2	2	no	—
1183	C₂×D₄	—	2	2	no	—
1184	C₂×D₄	—	2	2	no	—
1185	C₂×D₄	—	2	2	no	—
1186	C₂×D₄	—	2	2	no	—
1187	C₂×D₄	—	4	1	no	—
1188	C₂×D₄	—	4	1	no	—
1189	C₂×D₄	—	4	1	no	—
1190	C₂×D₄	—	4	1	no	—
1191	C₂×D₄	—	4	1	no	—
1192	C₂×D₄	—	4	1	no	—
1193	C₂×D₄	—	4	1	no	—
1194	C₂×D₄	—	4	1	no	—
1195	C₂×D₄	—	4	1	no	—
1196	C₂×D₄	—	4	1	no	—
1197	C₂×D₄	—	4	1	no	—
1198	C₂×D₄	—	4	1	no	—
1199	C₂×D₄	—	4	1	no	—
1200	C₂×D₄	—	4	1	no	—
1201	C₂×D₄	—	4	1	no	—
1202	C₂×D₄	—	4	1	no	—
1203	C₂×D₄	—	4	1	no	—
1204	C₂×D₄	—	4	1	no	—
1205	C₂×D₄	—	4	1	no	—
1206	C₂×D₄	—	4	1	no	—
1207	C₂×D₄	—	4	1	no	—
1208	C₂×D₄	—	4	1	no	—
1209	C₂×D₄	—	4	1	no	—
1210	C₂×D₄	—	4	1	no	—
1211	C₂×D₄	—	4	1	no	—
1212	C₂×D₄	—	4	1	no	—
1213	C₂²×C₄	—	2	2	no	—
1214	C₂²×C₄	—	2	2	no	—
1215	C₂²×C₄	—	2	2	no	—
1216	C₂²×C₄	—	2	2	no	—
1217	C₂²×C₄	—	2	2	no	—
1218	C₂²×C₄	—	2	2	no	—
1219	C₂²×C₄	—	2	2	no	—
1220	C₂²×C₄	—	2	2	no	—
1221	C₂²×C₄	—	2	2	no	—
1222	C₂²×C₄	—	2	2	no	—
1223	C₂²×C₄	—	4	1	no	—
1224	C₂²×C₄	—	4	1	no	—
1225	C₂²×C₄	—	4	1	no	—
1226	C₂²×C₄	—	4	1	no	—
1227	C₂²×C₄	—	4	1	no	—
1228	C₂²×C₄	—	4	1	no	—
1229	C₂²×C₄	—	4	1	no	—
1230	C₂²×C₄	—	4	1	no	—
1231	C₂²×C₄	—	4	1	no	—
1232	C₂²×C₄	—	4	1	no	—
1233	C₂²×C₄	—	4	1	no	—
1234	C₂²×C₄	—	4	1	no	—
1235	C₂²×C₄	—	4	1	no	—
1236	C₂²×C₄	—	4	1	no	—
1237	C₂²×C₄	—	4	1	no	—
1238	C₂²×C₄	—	4	1	no	—
1239	C₂²×C₄	—	4	16	no	—
1240	C₂²×C₄	#41×C₅₃	1	4	yes	—
1241	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1242	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1243	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1244	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1245	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1246	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1247	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1248	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1249	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1250	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1251	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1252	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1253	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1254	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1255	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1256	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1257	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1258	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1259	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1260	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1261	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1262	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1263	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1264	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1265	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1266	C₄⋊C₄	—	2	2	no	—
1267	C₄⋊C₄	—	2	2	no	—
1268	C₄⋊C₄	—	2	2	no	—
1269	C₄⋊C₄	—	2	2	no	—
1270	C₄⋊C₄	—	2	2	no	—
1271	C₄⋊C₄	—	2	2	no	—
1272	C₄⋊C₄	—	4	1	no	—
1273	C₄⋊C₄	—	4	1	no	—
1274	C₄⋊C₄	—	4	1	no	—
1275	C₄⋊C₄	—	4	1	no	—
1276	C₄⋊C₄	—	4	1	no	—
1277	C₄⋊C₄	—	4	1	no	—
1278	C₄⋊C₄	—	4	1	no	—
1279	C₄⋊C₄	—	4	1	no	—
1280	C₄⋊C₄	—	4	1	no	—
1281	C₄⋊C₄	—	4	1	no	—
1282	C₄⋊C₄	—	4	1	no	—
1283	C₄⋊C₄	—	4	1	no	—
1284	C₄⋊C₄	—	4	1	no	—
1285	C₄⋊C₄	—	4	1	no	—
1286	C₄⋊C₄	—	4	1	no	—
1287	C₄⋊C₄	—	4	1	no	—
1288	C₄⋊C₄	—	4	1	no	—
1289	C₄⋊C₄	—	4	1	no	—
1290	C₂²⋊C₄	—	2	2	no	—
1291	C₂²⋊C₄	—	2	2	no	—
1292	C₂²⋊C₄	—	2	2	no	—
1293	C₂²⋊C₄	—	2	2	no	—
1294	C₂²⋊C₄	—	2	2	no	—
1295	C₂²⋊C₄	—	2	2	no	—
1296	C₂²⋊C₄	—	2	2	no	—
1297	C₂²⋊C₄	—	2	2	no	—
1298	C₂²⋊C₄	—	2	2	no	—
1299	C₂²⋊C₄	—	2	2	no	—
1300	C₂²⋊C₄	—	2	2	no	—
1301	C₂²⋊C₄	—	2	2	no	—
1302	C₂²⋊C₄	—	2	2	no	—
1303	C₂²⋊C₄	—	2	2	no	—
1304	C₂²⋊C₄	—	2	2	no	—
1305	C₂²⋊C₄	—	2	2	no	—
1306	C₂²⋊C₄	—	4	1	no	—
1307	C₂²⋊C₄	—	4	1	no	—
1308	C₂²⋊C₄	—	4	1	no	—
1309	C₂²⋊C₄	—	4	1	no	—
1310	C₂²⋊C₄	—	4	1	no	—
1311	C₂²⋊C₄	—	4	1	no	—
1312	C₂²⋊C₄	—	4	1	no	—
1313	C₂²⋊C₄	—	4	1	no	—
1314	C₂²⋊C₄	—	4	1	no	—
1315	C₂²⋊C₄	—	4	1	no	—
1316	C₂²⋊C₄	—	4	1	no	—
1317	C₂²⋊C₄	—	4	1	no	—
1318	C₂²⋊C₄	—	4	1	no	—
1319	C₂²⋊C₄	—	4	1	no	—
1320	C₂²⋊C₄	—	4	1	no	—
1321	C₂²⋊C₄	—	4	1	no	—
1322	C₂²⋊C₄	—	4	1	no	—
1323	C₂²⋊C₄	—	4	1	no	—
1324	C₂²⋊C₄	—	4	1	no	—
1325	C₂²⋊C₄	—	4	1	no	—
1326	C₂²⋊C₄	—	4	1	no	—
1327	C₂²⋊C₄	—	4	1	no	—
1328	C₂²⋊C₄	—	4	1	no	—
1329	C₂²⋊C₄	—	4	1	no	—
1330	C₂²⋊C₄	—	4	1	no	—
1331	C₂²⋊C₄	—	4	1	no	—
1332	C₂²⋊C₄	—	4	1	no	—
1333	C₂²⋊C₄	—	4	1	no	—
1334	C₂²⋊C₄	—	4	1	no	—
1335	C₂²⋊C₄	—	4	1	no	—
1336	C₂²⋊C₄	—	4	1	no	—
1337	C₂²⋊C₄	—	4	1	no	—
1338	C₂²⋊C₄	—	4	1	no	—
1339	C₂²⋊C₄	—	4	1	no	—
1340	C₂²⋊C₄	—	4	1	no	—
1341	C₂²⋊C₄	—	4	1	no	—
1342	C₂²⋊C₄	—	4	1	no	—
1343	C₂²⋊C₄	—	4	1	no	—
1344	C₄²	—	4	1	no	—
1345	C₄²	—	4	1	no	—
1346	C₄²	—	4	1	no	—
1347	C₄²	—	4	1	no	—
1348	C₄²	—	4	1	no	—
1349	C₄²	—	4	1	no	—
1350	C₄²	—	4	1	no	—
1351	C₄²	—	4	1	no	—
1352	C₄²	—	4	1	no	—
1353	C₂³	—	2	1	no	—
1354	C₂³	—	2	1	no	—
1355	C₂³	—	2	1	no	—
1356	C₂³	—	2	1	no	—
1357	C₂³	—	2	1	no	—
1358	C₂³	—	2	1	no	—
1359	C₂³	—	2	1	no	—
1360	C₂³	—	2	1	no	—
1361	C₂³	—	2	1	no	—
1362	C₂³	—	2	1	no	—
1363	C₂³	—	2	1	no	—
1364	C₂³	—	2	1	no	—
1365	C₂³	—	2	1	no	—
1366	C₂³	—	2	1	no	—
1367	C₂³	—	2	1	no	—
1368	C₂³	—	2	1	no	—
1369	C₂³	—	2	1	no	—
1370	C₂³	—	2	1	no	—
1371	C₂³	—	2	1	no	—
1372	C₂³	—	2	1	no	—
1373	C₂³	—	2	1	no	—
1374	C₂³	—	2	1	no	—
1375	C₂³	—	2	1	no	—
1376	C₂³	—	2	1	no	—
1377	C₂³	—	2	1	no	—
1378	C₂³	—	2	1	no	—
1379	C₂³	—	2	1	no	—
1380	C₂³	—	2	1	no	—
1381	C₂³	—	2	1	no	—
1382	C₂³	—	2	1	no	—
1383	C₂³	—	2	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	1	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	4	4	no	—
1393	C₂³	—	4	4	no	—
1394	C₂³	—	4	4	no	—
1395	C₂³	—	4	4	no	—
1396	C₂³	—	4	4	no	—
1397	C₂³	—	4	4	no	—
1398	C₂³	—	4	4	no	—
1399	C₂³	C₂×#41×C₅₃	1	2	yes	—
1400	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1401	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1402	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1403	Q₈	—	8	2	no	—
1404	Q₈	—	8	2	no	—
1405	D₄	—	8	2	no	—
1406	D₄	—	8	2	no	—
1407	D₄	—	8	2	no	—
1408	D₄	—	8	2	no	—
1409	D₄	—	8	2	no	—
1410	D₄	—	8	2	no	—
1411	D₄	—	8	2	no	—
1412	D₄	—	8	2	no	—
1413	D₄	—	8	2	no	—
1414	D₄	—	8	2	no	—
1415	D₄	—	8	2	no	—
1416	D₄	—	8	2	no	—
1417	C₂×C₄	—	2	8	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	4	4	no	—
1491	C₂×C₄	—	4	4	no	—
1492	C₂×C₄	—	4	4	no	—
1493	C₂×C₄	—	4	4	no	—
1494	C₂×C₄	—	4	4	no	—
1495	C₂×C₄	—	8	2	no	—
1496	C₂×C₄	—	8	2	no	—
1497	C₂×C₄	—	8	2	no	—
1498	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1499	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1500	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1501	C₂²	—	2	2	no	—
1502	C₂²	—	2	2	no	—
1503	C₂²	—	2	2	no	—
1504	C₂²	—	2	2	no	—
1505	C₂²	—	2	2	no	—
1506	C₂²	—	2	2	no	—
1507	C₂²	—	2	2	no	—
1508	C₂²	—	2	2	no	—
1509	C₂²	—	2	2	no	—
1510	C₂²	—	4	16	no	—
1511	C₂²	—	4	1	no	—
1512	C₂²	—	4	1	no	—
1513	C₂²	—	4	1	no	—
1514	C₂²	—	4	1	no	—
1515	C₂²	—	4	1	no	—
1516	C₂²	—	4	1	no	—
1517	C₂²	—	4	1	no	—
1518	C₂²	—	4	1	no	—
1519	C₂²	—	4	1	no	—
1520	C₂²	—	4	1	no	—
1521	C₂²	—	4	1	no	—
1522	C₂²	—	4	1	no	—
1523	C₂²	—	4	1	no	—
1524	C₂²	—	4	1	no	—
1525	C₂²	—	4	1	no	—
1526	C₂²	—	4	1	no	—
1527	C₂²	—	4	1	no	—
1528	C₂²	—	4	1	no	—
1529	C₂²	—	4	1	no	—
1530	C₂²	—	4	1	no	—
1531	C₂²	—	4	1	no	—
1532	C₂²	—	4	1	no	—
1533	C₂²	—	4	1	no	—
1534	C₂²	—	4	1	no	—
1535	C₂²	—	4	1	no	—
1536	C₂²	—	4	1	no	—
1537	C₂²	—	4	1	no	—
1538	C₂²	—	4	1	no	—
1539	C₂²	—	4	1	no	—
1540	C₂²	—	4	1	no	—
1541	C₂²	—	4	1	no	—
1542	C₂²	—	4	1	no	—
1543	C₂²	—	4	1	no	—
1544	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1545	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1546	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1547	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1548	C₂²	C₅₃×#585	1	1	yes	characteristic
1549	C₂²	C₅₃×#585	1	1	yes	characteristic
1550	C₂²	C₅₃×#585	1	1	yes	characteristic
1551	C₄	—	2	2	no	—
1552	C₄	—	2	2	no	—
1553	C₄	—	2	2	no	—
1554	C₄	—	4	1	no	—
1555	C₄	—	4	1	no	—
1556	C₄	—	4	1	no	—
1557	C₄	—	4	1	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	1	no	—
1560	C₄	—	4	1	no	—
1561	C₄	—	4	1	no	—
1562	C₄	—	4	1	no	—
1563	C₄	—	4	1	no	—
1564	C₄	—	4	1	no	—
1565	C₄	—	4	1	no	—
1566	C₄	—	4	1	no	—
1567	C₄	—	4	1	no	—
1568	C₄	—	4	1	no	—
1569	C₄	—	4	1	no	—
1570	C₄	—	4	1	no	—
1571	C₄	—	4	1	no	—
1572	C₄	—	4	1	no	—
1573	C₄	—	4	1	no	—
1574	C₄	—	4	1	no	—
1575	C₄	—	4	1	no	—
1576	C₂	—	4	2	no	—
1577	C₂	—	4	2	no	—
1578	C₂	—	4	2	no	—
1579	C₂	—	8	1	no	—
1580	C₂	—	8	1	no	—
1581	C₂	—	8	1	no	—
1582	C₂	C₅₃×#3455	1	1	yes	characteristic
1583	C₂	C₅₃×#3490	1	1	yes	characteristic
1584	C₂	C₅₃×#3494	1	1	yes	characteristic
1585	C₂	C₅₃×#3533	1	1	yes	characteristic
1586	C₂	C₅₃×#3534	1	1	yes	characteristic
1587	C₂	C₅₃×#3540	1	1	yes	characteristic
1588	C₂	C₅₃×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#2849	C₂	semidirect
2. C₅₃×#2847	C₂	semidirect
3. C₅₃×#2747	C₂	semidirect
4. C₅₃×#2740	C₂	semidirect
5. C₅₃×#2739	C₂	semidirect
6. C₅₃×#2737	C₂	semidirect
7. C₅₃×#2737	C₂	semidirect
8. C₅₃×#2717	C₂	semidirect
9. C₅₃×#2703	C₂	semidirect
10. C₅₃×#2697	C₂	semidirect
11. C₅₃×#2696	C₂	semidirect
12. C₅₃×#2693	C₂	semidirect
13. C₅₃×#2688	C₂	semidirect
14. C₅₃×#2686	C₂	semidirect
15. C₅₃×#2684	C₂	semidirect
16. C₅₃×#2678	C₂	semidirect
17. C₅₃×#2672	C₂	semidirect
18. C₅₃×#2670	C₂	semidirect
19. C₅₃×#2665	C₂	semidirect
20. C₅₃×#2661	C₂	semidirect
21. C₅₃×#2597	C₂	semidirect
22. C₅₃×#2578	C₂	semidirect
23. C₅₃×#2557	C₂	semidirect
24. C₅₃×#2557	C₂	semidirect
25. C₅₃×#2477	C₂	semidirect
26. C₅₃×#2476	C₂	semidirect
27. C₅₃×#2474	C₂	semidirect
28. C₅₃×#2471	C₂	semidirect
29. C₅₃×#2335	C₂	semidirect
30. C₅₃×#2333	C₂	semidirect
31. C₅₃×#2280	C₂	semidirect
40. C₂×#123×C₅₃	C₂²	semidirect
41. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
51. C₅₃×#400	C₂²	semidirect
52. C₅₃×#400	C₂²	semidirect
53. C₅₃×#400	C₂²	semidirect
54. C₅₃×#400	C₂²	semidirect
55. C₅₃×#400	C₂²	semidirect
56. C₅₃×#399	C₂²	semidirect
57. C₅₃×#398	C₂²	semidirect
58. C₅₃×#398	C₂²	semidirect
64. C₅₃×#397	C₂²	semidirect
65. C₅₃×#397	C₂²	semidirect
66. C₅₃×#397	C₂²	semidirect
67. C₅₃×#397	C₂²	semidirect
68. C₅₃×#397	C₂²	semidirect
69. C₅₃×#397	C₂²	semidirect
70. C₅₃×#397	C₂²	semidirect
74. C₅₃×#396	C₂²	semidirect
75. C₅₃×#395	C₂²	semidirect
76. C₅₃×#395	C₂²	semidirect
77. C₅₃×#395	C₂²	semidirect
86. C₅₃×#394	C₂²	semidirect
87. C₅₃×#394	C₂²	semidirect
91. C₅₃×#393	C₂²	semidirect
92. C₅₃×#393	C₂²	semidirect
98. C₅₃×#392	C₂²	semidirect
99. C₅₃×#391	C₂²	semidirect
100. C₅₃×#391	C₂²	semidirect
106. C₅₃×#390	C₂²	semidirect
107. C₅₃×#390	C₂²	semidirect
108. C₅₃×#389	C₂²	semidirect
116. C₅₃×#388	C₂²	semidirect
117. C₅₃×#388	C₂²	semidirect
118. C₅₃×#388	C₂²	semidirect
119. C₅₃×#388	C₂²	semidirect
120. C₅₃×#388	C₂²	semidirect
121. C₅₃×#388	C₂²	semidirect
122. C₅₃×#388	C₂²	semidirect
123. C₅₃×#388	C₂²	semidirect
124. C₅₃×#388	C₂²	semidirect
125. C₅₃×#387	C₂²	semidirect
126. C₅₃×#387	C₂²	semidirect
127. C₅₃×#387	C₂²	semidirect
128. C₅₃×#387	C₂²	semidirect
129. C₅₃×#387	C₂²	semidirect
130. C₅₃×#387	C₂²	semidirect
131. C₅₃×#387	C₂²	semidirect
132. C₅₃×#387	C₂²	semidirect
133. C₅₃×#387	C₂²	semidirect
134. C₅₃×#387	C₂²	semidirect
135. C₅₃×#387	C₂²	semidirect
136. C₅₃×#387	C₂²	semidirect
153. C₅₃×#386	C₂²	semidirect
154. C₅₃×#386	C₂²	semidirect
155. C₅₃×#386	C₂²	semidirect
156. C₅₃×#386	C₂²	semidirect
161. C₅₃×#385	C₂²	semidirect
162. C₅₃×#385	C₂²	semidirect
163. C₅₃×#383	C₂²	semidirect
175. C₅₃×#380	C₂²	semidirect
179. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
184. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
185. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
706. #36735	C₅₃	direct (N × H)
782. #2849	C₂×C₅₃	semidirect
783. #2847	C₂×C₅₃	semidirect
784. #2747	C₂×C₅₃	semidirect
785. #2740	C₂×C₅₃	semidirect
786. #2739	C₂×C₅₃	semidirect
787. #2737	C₂×C₅₃	semidirect
788. #2737	C₂×C₅₃	semidirect
789. #2717	C₂×C₅₃	semidirect
790. #2703	C₂×C₅₃	semidirect
791. #2697	C₂×C₅₃	semidirect
792. #2696	C₂×C₅₃	semidirect
793. #2693	C₂×C₅₃	semidirect
794. #2688	C₂×C₅₃	semidirect
795. #2686	C₂×C₅₃	semidirect
796. #2684	C₂×C₅₃	semidirect
797. #2678	C₂×C₅₃	semidirect
798. #2672	C₂×C₅₃	semidirect
799. #2670	C₂×C₅₃	semidirect
800. #2665	C₂×C₅₃	semidirect
801. #2661	C₂×C₅₃	semidirect
802. #2597	C₂×C₅₃	semidirect
803. #2578	C₂×C₅₃	semidirect
804. #2557	C₂×C₅₃	semidirect
805. #2557	C₂×C₅₃	semidirect
806. #2477	C₂×C₅₃	semidirect
807. #2476	C₂×C₅₃	semidirect
808. #2474	C₂×C₅₃	semidirect
809. #2471	C₂×C₅₃	semidirect
810. #2335	C₂×C₅₃	semidirect
811. #2333	C₂×C₅₃	semidirect
812. #2280	C₂×C₅₃	semidirect
834. C₂×#123	C₂²×C₅₃	semidirect
835. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
845. #400	C₂²×C₅₃	semidirect
846. #400	C₂²×C₅₃	semidirect
847. #400	C₂²×C₅₃	semidirect
848. #400	C₂²×C₅₃	semidirect
849. #400	C₂²×C₅₃	semidirect
850. #399	C₂²×C₅₃	semidirect
851. #398	C₂²×C₅₃	semidirect
852. #398	C₂²×C₅₃	semidirect
858. #397	C₂²×C₅₃	semidirect
859. #397	C₂²×C₅₃	semidirect
860. #397	C₂²×C₅₃	semidirect
861. #397	C₂²×C₅₃	semidirect
862. #397	C₂²×C₅₃	semidirect
863. #397	C₂²×C₅₃	semidirect
864. #397	C₂²×C₅₃	semidirect
868. #396	C₂²×C₅₃	semidirect
869. #395	C₂²×C₅₃	semidirect
870. #395	C₂²×C₅₃	semidirect
871. #395	C₂²×C₅₃	semidirect
880. #394	C₂²×C₅₃	semidirect
881. #394	C₂²×C₅₃	semidirect
885. #393	C₂²×C₅₃	semidirect
886. #393	C₂²×C₅₃	semidirect
892. #392	C₂²×C₅₃	semidirect
893. #391	C₂²×C₅₃	semidirect
894. #391	C₂²×C₅₃	semidirect
900. #390	C₂²×C₅₃	semidirect
901. #390	C₂²×C₅₃	semidirect
902. #389	C₂²×C₅₃	semidirect
910. #388	C₂²×C₅₃	semidirect
911. #388	C₂²×C₅₃	semidirect
912. #388	C₂²×C₅₃	semidirect
913. #388	C₂²×C₅₃	semidirect
914. #388	C₂²×C₅₃	semidirect
915. #388	C₂²×C₅₃	semidirect
916. #388	C₂²×C₅₃	semidirect
917. #388	C₂²×C₅₃	semidirect
918. #388	C₂²×C₅₃	semidirect
919. #387	C₂²×C₅₃	semidirect
920. #387	C₂²×C₅₃	semidirect
921. #387	C₂²×C₅₃	semidirect
922. #387	C₂²×C₅₃	semidirect
923. #387	C₂²×C₅₃	semidirect
924. #387	C₂²×C₅₃	semidirect
925. #387	C₂²×C₅₃	semidirect
926. #387	C₂²×C₅₃	semidirect
927. #387	C₂²×C₅₃	semidirect
928. #387	C₂²×C₅₃	semidirect
929. #387	C₂²×C₅₃	semidirect
930. #387	C₂²×C₅₃	semidirect
947. #386	C₂²×C₅₃	semidirect
948. #386	C₂²×C₅₃	semidirect
949. #386	C₂²×C₅₃	semidirect
950. #386	C₂²×C₅₃	semidirect
955. #385	C₂²×C₅₃	semidirect
956. #385	C₂²×C₅₃	semidirect
957. #383	C₂²×C₅₃	semidirect
969. #380	C₂²×C₅₃	semidirect
973. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
978. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
979. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
980. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
981. C₅₃	#36735	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#2849	2
C₅₃×#2847	2
C₅₃×#2747	2
C₅₃×#2740	2
C₅₃×#2739	2
C₅₃×#2737	2
C₅₃×#2717	2
C₅₃×#2703	2
C₅₃×#2697	2
C₅₃×#2696	2
C₅₃×#2693	2
C₅₃×#2688	2
C₅₃×#2686	2
C₅₃×#2684	2
C₅₃×#2678	2
C₅₃×#2672	2
C₅₃×#2670	2
C₅₃×#2665	2
C₅₃×#2661	2
C₅₃×#2597	2
C₅₃×#2578	2
C₅₃×#2557	2
C₅₃×#2477	2
C₅₃×#2476	2
C₅₃×#2474	2
C₅₃×#2471	2
C₅₃×#2335	2
C₅₃×#2333	2
C₅₃×#2280	2
#36735	53

Subgroups — C53×#36735 #27244247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36735 #27244247